Journal of Convex Analysis 28 (2021), No. 4, 1053--1072
Copyright Heldermann Verlag 2021
Screening Rules and its Complexity for Active Set Identification
Eugene Ndiaye
Riken AIP, Japan
eugene.ndiaye@riken.jp
Olivier Fercoq
LTCI, Télécom Paris, and: Institut Polytechnique de Paris, Palaiseau, France
olivier.fercoq@telecom-paris.fr
Joseph Salmon
IMAG, Université Montpellier, France
joseph.salmon@umontpellier.fr
Screening rules were recently introduced as a technique for explicitly identifying active structures such as sparsity, in optimization problem arising in machine learning. This has led to new methods of acceleration based on a substantial dimension reduction. We show that screening rules stem from a combination of natural properties of subdifferential sets and optimality conditions, and can hence be understood in a unified way. Under mild assumptions, we analyze the number of iterations needed to identify the optimal active set for any converging algorithm. We show that it only depends on its convergence rate.
Keywords: Convex optimization, screening rules, active set identification, nonsmooth optimization.
MSC: 49M29, 65K05, 90C06, 90C25.
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